# std::expint, std::expintf, std::expintl

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< cpp‎ | experimental‎ | special functions

double expint( double arg ); double expint( float arg ); double expint( long double arg ); float expintf( float arg ); long double expintl( long double arg ); | (1) |
double expint( IntegralType arg ); | (2) |

1) Computes the exponential integral of arg.
2) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (1) after casting the argument to double.

As all special functions, `expint` is only guaranteed to be available in `<cmath>` if `__STDCPP_MATH_SPEC_FUNCS__` is defined by the implementation to a value at least 201003L and if the user defines `__STDCPP_WANT_MATH_SPEC_FUNCS__` before including any standard library headers.

### Parameters

arg | - | value of a floating-point or Integral type

### Return value

If no errors occur, value of the exponential integral of arg, that is -∫∞
-arg

e-t
t

dt, is returned.

### Error handling

Errors may be reported as specified in math_errhandling.

- If the argument is NaN, NaN is returned and domain error is not reported.
- If the argument is ±0, -∞ is returned.

### Notes

Implementations that do not support TR 29124 but support TR 19768, provide this function in the header `tr1/cmath` and namespace `std::tr1`.

An implementation of this function is also available in boost.math.

### Example

(works as shown with gcc 6.0)

Run this code

    #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
    #include <cmath>
    #include <iostream>

    int main()
    {
        std::cout << "Ei(0) = " << std::expint(0) << '\n'
                  << "Ei(1) = " << std::expint(1) << '\n'
                  << "Gompetz constant = " << -std::exp(1) * std::expint(-1) << '\n';
    }

Output:

    Ei(0) = -inf
    Ei(1) = 1.89512
    Gompetz constant = 0.596347

### External links

Weisstein, Eric W. "Exponential Integral." From MathWorld--A Wolfram Web Resource.

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